Multiple choice

If the equation ax2 + bx + c = 0 has no real roots and a + b + c < 0,

  1. c = 0

  2. c > 0

  3. c < 0

  4. c = ab
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

If a quadratic has no real roots, the parabola never crosses the x-axis, meaning it is always above or below the axis. Since a+b+c < 0 (the value of the function at x=1 is negative), the parabola must be entirely below the x-axis, implying a < 0. For a parabola to be entirely below the x-axis, its y-intercept c must also be negative.

AI explanation

Since the quadratic equation has no real roots, its graph does not cross the x-axis and the sign of 'a' matches the sign of 'c', meaning a and c have the same sign. Evaluating the quadratic at x = 1 gives a(1)^2 + b(1) + c < 0, so a + b + c is negative. Because 'a' must be negative to keep the parabola entirely below or above the x-axis in a way that makes the sum at x=1 negative, 'c' must also be negative.

Keep practicing — related questions